Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues

Jean-Pierre Antoine and Camillo Trapani ()
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Jean-Pierre Antoine: Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
Camillo Trapani: Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi n. 34, I-90123 Palermo, Italy

Mathematics, 2022, vol. 11, issue 1, 1-11

Abstract: Given a self-adjoint operator A in a Hilbert space H , we analyze its spectral behavior when it is expressed in terms of generalized eigenvectors. Using the formalism of Gel’fand distribution bases, we explore the conditions for the generalized eigenspaces to be one-dimensional, i.e., for A to have a simple spectrum.

Keywords: rigged Hilbert space; generalized eigenvectors; simple spectrum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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